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Abstract:

Electric power grid monitoring methods and apparatus are described.
According to one aspect, an electric power grid signal processing method
includes accessing a plurality of signals which are individually
indicative of a characteristic of electromechanical energy within an
electric power grid, using the plurality of signals, generating a
composite signal, and analyzing the composite signal to provide
information regarding an oscillatory mode within the electric power
system.

Claims:

1. An electric power grid signal processing method comprising: accessing
a plurality of signals which are individually indicative of a
characteristic of electromechanical energy within an electric power grid;
using the plurality of signals, generating a composite signal; and
analyzing the composite signal to provide information regarding an
oscillatory mode within the electric power system.

2. The method of claim 1 further comprising accessing the signals which
are indicative of the characteristic of electromechanical energy from
different geographical locations of the electric power system.

3. The method of claim 1 wherein the generating comprises generating the
composite signal using data within the signals which is synchronized with
respect to time.

4. The method of claim 1 further comprising: identifying the oscillatory
mode which is of interest to be analyzed; and selecting the signals using
the oscillatory mode of interest to be analyzed.

5. The method of claim 4 wherein the oscillatory mode is a first
oscillatory mode of interest and the signals are a first set of signals,
and further comprising: identifying a second oscillatory mode of interest
to be analyzed; and selecting a second set of signals using the second
oscillatory mode of interest to be analyzed, and wherein the first and
second sets of signals are different.

6. The method of claim 1 further comprising weighting the signals such
that information within the signals regarding the mode of interest is
increased and information regarding other modes is decreased.

7. An oscillatory mode estimation method comprising: processing a signal
which is indicative of electromechanical energy within an electric power
grid; analyzing the signal which is indicative of the electromechanical
energy using an analysis function to estimate an oscillatory mode of
interest upon the electric power grid, wherein the analyzing comprises
analyzing in accordance with results of the processing of the signal.

8. The method of claim 7 further comprising, as a result of the
processing, selecting one of a plurality of values for a parameter of the
analysis function.

9. The method of claim 8 wherein the values of the parameter define
respective different amounts of data of the signal to be analyzed using
the analysis function.

10. The method of claim 9 further comprising selecting the one of the
values which specifies use of the least amount of data of the signal.

11. The method of claim 7 wherein the analyzing comprises analyzing the
signal a plurality of times using a plurality of different values of a
parameter of the analysis function to provide different estimates of the
oscillatory mode of interest before the selecting, and further comprising
selecting one of the estimates of the oscillatory mode in accordance with
the results of the processing of the signal.

12. The method of claim 7 wherein the analyzing comprises analyzing the
signal using the analysis function in parallel using the different
amounts of data, and selecting results of one of the parallel analyses of
the signal in accordance with the processing of the signal.

13. The method of claim 7 wherein the signal comprises a composite
signal, and further comprising combining a plurality of signals which are
individually indicative of a characteristic of electromechanical energy
within the electric power grid to generate the composite signal.

14. The method of claim 7 wherein the processing comprises determining an
amount of electromechanical energy present within the signal which
corresponds to the oscillatory mode of interest, and wherein the
analyzing comprises analyzing in accordance with the amount of
electromechanical energy present within the signal.

15. The method of claim 7 wherein the processing comprises determining an
amount of damping of the oscillatory mode of interest, and wherein the
analyzing comprises analyzing in accordance with the amount of damping
present within the signal.

16. A mode shape estimation method comprising: identifying a frequency of
an oscillatory mode of interest within an electric power grid; and
analyzing a signal which is indicative of electromechanical energy within
the electric power grid using a mode shape estimation function in
accordance with the frequency of the oscillatory mode of interest.

17. The method of claim 16 wherein the analyzing the signal in accordance
with the frequency of the oscillatory mode of interest comprises only
analyzing the signal using the mode shape estimation function at the
frequency of the oscillatory mode of interest and not analyzing the
signal at other frequencies.

18. The method of claim 16 further comprising: defining a plurality of
frequency bins of a frequency spectrum; and selecting one or more of the
frequency bins corresponding to the frequency of the oscillatory mode of
interest, and wherein the analyzing comprises analyzing the signal using
the mode shape estimation function at the one or more of the selected
frequency bins.

19. The method of claim 16 wherein the signal comprises a composite
signal, and further comprising combining a plurality of signals which are
individually indicative of a characteristic of electromechanical energy
within the electric power grid to generate the composite signal.

20. The method of claim 16 wherein the analyzing identifies a phase of a
generator which participates in the oscillatory mode of interest.

Description:

TECHNICAL FIELD

[0001] This disclosure relates to electric power grid monitoring methods
and apparatus.

BACKGROUND OF THE DISCLOSURE

[0002] Electromechanical oscillations occur within an interconnected
synchronized electric power grid when two or more rotating machines
(e.g., generators), perhaps at great geographical distance from one
another, exchange energy. Oscillations are manifested within the electric
power grid as dynamically changing power delivery patterns over the bulk
electric transmission grid. Undamped or excessive oscillatory energy
within an interconnected electric power grid can cause catastrophic
failure of the grid resulting in widespread "blackouts." The frequencies,
damping, shape, and magnitude of the oscillatory energy present within an
interconnected electric power grid at any given time, regardless of
whether the oscillations ultimately result in a blackout, are indicators
of system stress. Accordingly, it is prudent and useful to monitor these
parameters within an interconnected electric power grid.

[0003] The disclosure is directed towards apparatus and methods for
monitoring electromechanical oscillations within an electric power grid.

BRIEF DESCRIPTION OF THE DRAWINGS

[0004] Exemplary embodiments of the disclosure are described below with
reference to the following accompanying drawings.

[0005] FIG. 1 is a functional block diagram of an electrical system
according to one embodiment.

[0006]FIG. 2 is a functional block diagram of a computing device
according to one embodiment.

[0007]FIG. 3 is a functional block diagram of a method of monitoring
oscillatory energy in the electrical system according to one embodiment.

[0008]FIG. 4 is a flow chart of a method of generating a composite signal
according to one embodiment.

[0009] FIG. 5 is a flow chart of a method of selecting an appropriate
window size of data to monitor oscillatory energy according to one
embodiment.

DETAILED DESCRIPTION OF THE DISCLOSURE

[0010] This disclosure is submitted in furtherance of the constitutional
purposes of the U.S. Patent Laws "to promote the progress of science and
useful arts" (Article 1, Section 8).

[0011] According to one embodiment, an electric power grid signal
processing method comprises accessing a plurality of signals which are
individually indicative of a characteristic of electromechanical energy
within an electric power grid, using the plurality of signals, generating
a composite signal, and analyzing the composite signal to provide
information regarding an oscillatory mode within the electric power
system.

[0012] According to another embodiment, an oscillatory mode estimation
method comprises processing a signal which is indicative of
electromechanical energy within an electric power grid, analyzing the
signal which is indicative of the electromechanical energy using an
analysis function to estimate an oscillatory mode of interest upon the
electric power grid, wherein the analyzing comprises analyzing in
accordance with results of the processing of the signal.

[0013] According to an additional embodiment, a mode shape estimation
method comprises identifying a frequency of an oscillatory mode of
interest within an electric power grid and analyzing a signal which is
indicative of electromechanical energy within the electric power grid
using a mode shape estimation function in accordance with the frequency
of the oscillatory mode of interest.

[0014] Referring to FIG. 1, an example block diagram of a synchronous
electrical system 10 for delivering electric power is shown. The
illustrated example system 10 includes an electric power grid 12 which
transmits electric power from a plurality of generators 14 to consumer's
loads 16 where the delivered electric power is consumed. An example
electric power grid 12 may include transmission and distribution networks
which transmit electric power over significant distances and at
appropriate voltages for use by the loads 16. Although only two
generators 14 are shown, numerous generators 14 may be generating and
delivering electrical power to the electric power grid 12.

[0015] A plurality of monitoring devices 18 may monitor electric power
flowing through a plurality of points or nodes of the electric power grid
12. For example, the monitoring devices 18 may be configured to monitor
the electric power at substations, branching points and/or other desired
locations of the electric power grid 12. In one embodiment, the
monitoring devices 18 are implemented as phasor measurement units (PMUs)
which may monitor and sample phasors of the electric power grid 12 in the
form of magnitudes and phase angles of electrical characteristics, such
as currents and voltages. Measurements of the monitoring devices 18 may
be utilized to assist with the detection of potentially dangerous
oscillatory modes which may occur within electric power grid 12, for
example, when generators 14 or groups of generators 14 exchange energy,
perhaps over significant geographical distances (e.g., thousands of
miles).

[0016] Some analysis operations utilize samples from a plurality of
monitoring devices 18 which may be synchronized in time, and accordingly,
the monitoring devices 18 are configured to obtain at least some of the
samples at common points in time in one embodiment. In one embodiment,
the monitoring devices 18 may have internal clocks which are synchronized
with respect to one another, for example, using a global positioning
system (GPS).

[0017] A computing device 20 is coupled with the monitoring devices 18 and
is configured to process signals generated by the monitoring devices 18
as described further below. For example, the computing device 20 may
monitor the output of the monitoring devices 18 to identify the presence
of potentially dangerous oscillatory energy upon the electric power grid
12. Referring to FIG. 2, one example embodiment of a computing device 20
is shown and includes a user interface 22, processing circuitry 24,
storage circuitry 26 and a communications interface 28. Other embodiments
of computing device 20 are possible including more, less, and/or
alternative components.

[0018] User interface 22 is configured to interact with a user including
conveying data to a user (e.g., displaying visual images for observation
by the user) as well as receiving inputs from the user. User interface 22
may indicate operational conditions within the electrical system 10 and
may display or indicate warnings, for example, upon the detection of
potentially dangerous oscillatory modes which may be present within
electric power grid 12.

[0019] In one embodiment, processing circuitry 24 is arranged to process
data, control data access and storage, issue commands, and control other
desired operations. For example, processing circuitry 24 may process
signals from monitoring devices 18 as described in detail below.

[0020] Processing circuitry 24 may comprise circuitry configured to
implement desired programming provided by appropriate computer-readable
storage media in at least one embodiment. For example, the processing
circuitry 24 may be implemented as one or more processor(s) and/or other
structure configured to execute executable instructions including, for
example, software and/or firmware instructions. Other exemplary
embodiments of processing circuitry 24 include hardware logic, PGA, FPGA,
ASIC, state machines, and/or other structures alone or in combination
with one or more processor(s). These examples of processing circuitry 24
are for illustration and other configurations are possible.

[0021] Storage circuitry 26 is configured to store programming such as
executable code or instructions (e.g., software and/or firmware),
electronic data, databases, or other digital information and may include
computer-readable storage media. At least some embodiments or aspects
described herein may be implemented using programming stored within one
or more computer-readable storage medium of storage circuitry 26 and
configured to control appropriate processing circuitry 24.

[0022] The computer-readable storage medium may be embodied in one or more
articles of manufacture which can contain, store, or maintain
programming, data and/or digital information for use by or in connection
with an instruction execution system including processing circuitry 24 in
the exemplary embodiment. For example, exemplary computer-readable
storage media may include any one of physical media such as electronic,
magnetic, optical, electromagnetic, infrared or semiconductor media. Some
more specific examples of computer-readable storage media include, but
are not limited to, a portable magnetic computer diskette, such as a
floppy diskette, a zip disk, a hard drive, random access memory, read
only memory, flash memory, cache memory, and/or other configurations
capable of storing programming, data, or other digital information.

[0023] Communications interface 28 is arranged to implement communications
of computing system 10 with respect to external devices (such as
monitoring devices 18). Furthermore, computing device 20 may also
communicate with control facilities of the electric system 10, for
example, such that corrective action may be implemented in the presence
of potentially dangerous oscillatory modes within the electric power grid
12.

[0024] In one embodiment, communications interface 28 may be arranged to
communicate information bi-directionally with respect to computing device
20. Communications interface 28 may be implemented as a network interface
card (NIC), serial or parallel connection, USB port, Firewire interface,
flash memory interface, or any other suitable arrangement for
implementing communications with respect to computing device 20.

[0025] Referring to FIG. 3, a plurality of processing operations performed
by processing circuitry 24 of computing device 20 are described according
to one embodiment. Additional details of processing operations of FIG. 3
are also shown in the example methods of FIGS. 4-5. Among performing
other operations, the computing device 20 may process a plurality of data
signals generated by a plurality of monitoring devices 18 for use in
estimating oscillatory modes in terms of frequency, damping and shape in
at least one embodiment.

[0026] As shown in the example of FIG. 3, computing device 20 is
configured to access input 30 in the form of signals, also referred to as
samples, generated by the monitoring devices 18 in one embodiment. A
signal measured by a monitoring device 18 may be referred to as a
"synchrophasor" which may include information regarding one or more
characteristic of electromechanical energy of system 10 (e.g., a phasor
voltage or current in real/imaginary or magnitude/angle format). The
synchrophasors may include appropriate time stamps when they were
obtained and reporting rates of the respective measuring devices 18 in
one embodiment. The signals of input 30 may be accessed from monitoring
devices 18 which are selected based upon an oscillatory mode of interest
to be analyzed according to one embodiment.

[0027] One aspect of the disclosure is directed towards calculating one or
more composite signals, which may be referred to as pseudosynchrophasor
signals, that contain enhanced modal (or oscillatory) energy signatures
and which may be used to provide estimates of a mode's frequency and
damping within the electric power grid 12 of increased accuracy. The
shape is not calculated for the composite signal. In one embodiment, a
pseudosynchrophasor is a signal derived from combining and/or scaling
multiple synchrophasor signals as described in additional detail below.
In a more specific example, pseudosynchrophasor signals are generated by
combining and/or scaling a plurality of synchrophasor signals, for
example, which may include linearly combining signals having different
voltage angles or linearly combining real or reactive power signals. In
many electric power systems, a single synchrophasor signal may not
contain sufficient information content upon which to perform subsequent
analysis and which in turn may result in poor accuracy of modal estimates
(e.g., estimation of damping of a mode of interest). The created
pseudosynchrophasor signals may be processed using known techniques to
provide modal estimates of increased accuracy over analysis operations
which are based upon individual synchrophasor signals.

[0028] In the example of FIG. 3, the accessed signals of input 30 are
initially processed 34 using a window 32. The window 32 selects a
prescribed time history of the signals of input 30. For example, the past
10 seconds of the signals of input 30 are selected in one embodiment.
Other window sizes may be used in other embodiments.

[0029] The output is applied to preprocessing 36 where the signals may be
combined to form a composite signal as described in additional detail in
one embodiment in FIG. 4. The example preprocessing method of FIG. 4
calculates a composite signal for use in analyzing a mode of interest
according to one aspect of the disclosure. The illustrated example method
may be performed using the processing circuitry 24 in one embodiment.
Other methods are possible including more, less and/or alternative acts.

[0030] At an act A10, a mode of interest at a particular frequency is
identified. For example, a mode of interest may be identified using a
spectrum estimation algorithm or from a previous iteration of the output
54. Using previous research, certain modes may be known to be susceptible
to underdamping and may be monitored more closely than other modes.
Furthermore, the generators which participate in the mode may be known,
and accordingly, the synchrophasor signals utilized below may be selected
from monitoring devices 18 which monitor such participating generators.

[0031] At an act A12, the mode shape of the identified mode of interest is
estimated. The mode shape of the selected synchrophasor signals is
estimated or alternatively a previous iteration estimate from mode shape
estimation 53 may be used. Mode shape estimation analyzes the input
signals and mode frequency as inputs from mode-meter functions of the
selected monitoring devices 18 being analyzed and calculates the mode
shape for the identified mode of interest.

[0033] At an act A14, a plurality of signals may be selected which are to
be combined. The signals may be synchrophasor signals provided by the
monitoring devices 18, and accordingly, indicative of voltages, currents,
or other derived signals, such as power and frequency. In one embodiment,
the signals are selected from monitoring devices 18 which sample signals
from diverse geographical areas of the electric power grid 12, for
example, from different nodes of the electric power grid 12. In one
embodiment, the selected signals which are combined comprise data which
are synchronized with one another with respect to time (e.g., data
samples of the signals are synchronized with one another with respect to
time). In one implementation, signals with a relatively large mode-shape
amplitude are selected. For example, all signals with a mode-shape
amplitude greater than a threshold may be selected. A threshold may be
selected based upon engineering studies of historical data and/or
benchmark testing of the power system in one embodiment. In another
example, one might select a synchrophasor signal from a geographic region
with the largest mode-shape amplitude. Additional details regarding
selecting signals are described in D. Trudnowski, "Estimating
Electromechanical Mode Shape from Synchrophasor Measurements," IEEE
Transactions on Power Systems, vol. 23, no. 3, pp. 1188-1195, August
2008, the teachings of which are incorporated herein by reference.

[0034] At an act A16, weights are selected in the described method for
weighting of the signals before they are combined. The weighting factors
may be linear in one embodiment. In one embodiment, the weights are
selected such that in-phase signals are additive during combination
operations and anti-phase signals are subtractive providing an increased
coherent gain. For example, a synchrophasor signal provided by a
monitoring device 18 may include information regarding a plurality of
modes. The weights may be selected such that the information in the
signals regarding the mode of interest is increased when the signals are
combined while information regarding other modes (not of interest or
otherwise noise) is reduced or canceled.

[0035] In one more specific embodiment, weights are selected based upon
mode-shape amplitudes and angles to amplify modal energy of a desired
mode. For example, if the mode shape of synchrophasor 1 of interest is
180 degrees out of phase with the mode shape of synchrophasor 2 of
interest, the weight for synchrophasor 1 will be the negative of the
weight for synchrophasor 1. The synchrophasors are then linearly combined
using the calculated weights. In another example, a weight may be
selected as an inverse of a mode-shape amplitude of a signal (e.g.,
synchrophasor 1 may have a mode-shape amplitude of 0.1 with an angle of 0
degrees, and synchrophasor 2 may have mode-shape amplitude of 0.3 with an
angle of 180 degrees and the weights would then be 1/0.1 for
synchrophasor 1 and 1/0.3 for synchrophasor 2 in this example).

[0036] At an act A18, the signals are combined with the appropriate
weightings to form the composite signal (e.g., pseudosynchrophasor
signal), which has increased oscillatory energy content regarding the
mode of interest and yielding a more accurate estimate of energy content
for the mode of interest compared with an individual signal obtained from
a single monitoring device 18. The pseudosynchrophasor is representative
of oscillation energy (also referred to as modal energy) for the given
mode of interest and is a time-series signal calculated from plural
synchrophasor signals generated by a plurality of monitoring devices 18
which correspond to a mode of interest in the described embodiment. In
one example, the signals are multiplied by the weights and the weighted
signals are added.

[0037] At an act A20, the composite signal is output and may be used for
further analysis of the mode of interest.

[0038] For example, the composite signal may be processed using one or
more desired analytical techniques or functions to provide information
regarding the oscillatory mode of interest (e.g., frequency, damping,
shape). Example analytical techniques include a mode meter function, a
ringdown detector function, an oscillation trigger function or a mode
shape estimator function as described further below. The use of the
generated composite signal typically requires less fine tuning of the
analysis functions which are utilized and provides increased accuracy of
the analysis functions over a wider range of parameters compared with
executing the analysis functions upon synchrophasor signals without the
described pre-processing.

[0039] Referring again to 4, the output of the preprocessing 36 (i.e., the
composite signal) may be processed in parallel by plural processing
operations 40a-40n using a plurality of respective different window sizes
42a-42n which correspond to different amounts of data of the signal in
the described example method. The use of plural processing operations
40a-40n upon the different window sizes 42a-42n is implemented to attempt
to identify a reduced amount of information which may be processed while
still enabling satisfactory results to be obtained.

[0040] For example, if the analysis utilizes too much data, potentially
damaging oscillations may not be identified in sufficient time to permit
corrective action to be taken. Accordingly, the use of a smaller window
size may improve a response time as well as increase the chances that
changes of short duration corresponding to a potentially dangerous mode
may be identified. However, the results may be inaccurate if insufficient
data is utilized. As described further below, the composite signal may be
processed separately to determine which of the window sizes 42a-42n
should be utilized to provide improved (faster) response times while
still yielding acceptable results. While the present embodiment is
discussed with respect to parallel processing of a composite signal, the
parallel processing may also be performed upon other signals, such as
synchrophasors.

[0041] The illustrated processing operations multiply 44a-44n the
composite signal by the appropriate data window size (e.g., appropriate
time history of data to be utilized) 42a-42n to provide the different
amounts of data which will be processed by the respective analysis
function 46a-46n corresponding to the respective window sizes 42a-42n.
Example window sizes 42a-42n may be selected between an example range of
10 seconds-60 minutes for ringdown detection, oscillation trigger and
mode meter processing described below. Additional window sizes may also
be utilized and/or different window sizes may be utilized corresponding
to the analyses to be performed. In one embodiment, the different
processing operations 40a-40n operate upon data from the present moment
in time and going back in time as determined by the respective window
size 42a-42n for the respective processing operation 40a-40n.

[0042] One example of an analysis function 46a-46n for monitoring
oscillatory energy is called a mode meter function. A mode meter function
is an automated analysis approach which uses input signals to calculate a
given mode's frequency and damping under both ambient and transient
conditions. This method typically takes 2 min to 60 min of data. Examples
of mode meter functions which may be utilized include Yule-Walker, Robust
Recursive Least Squares (RRLS), and Regularize RRLS (R3LS), are described
in D. Trudnowski and J. W. Pierre, "Signal Processing Methods for
Estimating Small-Signal Dynamics Properties from Measured Responses,"
Chapter 1 of Inter-area Oscillation in Power Systems: A non-linear and
Nonstationary Perspective, Chapter 1, pp. 1-36, Springer, New York, 2009,
the teachings of which are incorporated herein by reference.

[0043] Another example of an analysis function 46a-46n for monitoring
oscillatory energy is called a ringdown detection function. A ringdown
detection function analyzes an input signal, detects an oscillation, and
estimates the modes (frequencies and respective dampings) contained in
the transient. Parameters estimated are the damping, frequency, and shape
of each mode in the transient. This approach typically utilizes
approximately 30 sec. of data. Details of example ring detection
functions are described in D. Trudnowski and J. Pierre, "Signal
Processing Methods for Estimating Small-Signal Dynamic Properties from
Measured Responses," Chapter 1 of Inter-area Oscillations in Power
Systems: A Nonlinear and Nonstationary Perspective, ISBN:
978-0-387-89529-1, Springer, 2009 and N. Zhou, Z. Huang, F. Tuffner, J.
W. Pierre, and S. Jin, "Automatic Implementation of Prony Analysis for
Electromechanical Mode Identification from Phasor Measurements,"
Proceedings of the IEEE Power Engineering Society General Meeting, July
2010, the teachings of which are incorporated herein by reference.

[0044] Another example of an analysis function 46a-46n for monitoring
oscillatory energy is called an oscillation trigger function. An
oscillation trigger function is an algorithm that uses information from
power spectral density calculations, possibly a mode meter, possibly
oscillation detection calculations, and filtered time-domain signals to
detect unusual oscillatory activity and provides notification of the
oscillatory activity to a visualization application for presentation to
an operator, engineer or other desired personnel. An example of an
oscillation trigger function is described in J. Hauer and F. Vakili, "An
Oscillation Detector used in the BPA Power System Disturbance Monitor,"
IEEE Trans. On Power Systems, vol. 5, no. 1, pp. 74-79, February 1990,
the teachings of which are incorporated herein by reference. Other
analysis functions may be also be utilized.

[0045] The outputs of the analysis functions 46a-46n are provided to
results selection processing 50. Processing 50 also receives the
composite signal outputted from preprocessing 36 and which may be
processed to perform the selection in the described embodiment. In one
embodiment, an amount of modal energy present in the range of the mode
frequency of interest and the damping may be used to determine an
appropriate window size. For example, if there is a certain amount of
modal energy present, then a corresponding window size may be selected as
determined by previous experiments and analysis of modes. In another
example, if the damping is known to be a certain amount, then a window
size which corresponds to the damping may be used as determined by
previous experiments and analysis of modes. Accordingly, the composite
signal may be processed as described with respect to FIG. 5 in one
embodiment and the results of the processing of the composite signal may
be utilized to determine the appropriate window size of data to be
processed by the analysis function.

[0046] Referring to FIG. 5, an example method performed during the results
selection processing 50 of FIG. 4 to select an appropriate window size is
described. The illustrated example method may be performed using the
processing circuitry 24 in one embodiment. The illustrated method is
described with respect to processing of a signal which is indicative of
oscillatory energy in a mode of interest (e.g., the composite signal
outputted from preprocessing 36, however, other signals such as a
synchrophasor signal may also be processed in other embodiments). Other
methods are possible including more, less and/or alternative acts.

[0047] At an act A30, the signal is filtered to identify an amount of
oscillation energy present in the signal. In one embodiment, an RMS
filter is used. The filtering provides information regarding the amount
of energy present in the received signal corresponding to the range of
the mode frequency of interest. In general, a relatively less amount of
data may be processed for a desired accuracy if there is a relatively
increased amount of energy present in the oscillation energy being
analyzed in one embodiment. An RMS filter which may be used performs
band-pass filtering in the range of the desired frequency, squaring the
result of the band-pass filtered output, low-pass filtering the squared
signal and calculating the square-root of the resulting low-pass filtered
signal. The resulting output is a measure of the RMS energy of the
original signal. In another embodiment, the squaring may be performed
upon an absolute value of the result of the band-pass filtered output.

[0048] At an act A32, the amount of energy present may be compared with
respect to one or more energy thresholds corresponding to energy levels
within the signal. In one embodiment, a plurality of energy thresholds
may be used corresponding to the respective window sizes which may be
utilized (e.g., the triggering of one threshold results in the selection
of a respective window size). Energy thresholds are selected based upon
engineering studies of historical data and/or benchmark testing of the
power system in one example.

[0049] At an act A34, it is determined whether the amount of oscillatory
energy present as determined from act A30 triggered (e.g., is greater
than) any of the energy thresholds.

[0050] If the result of act A34 is positive, then the processing proceeds
to act A36 to select the appropriate window size of the data to be
utilized. For example, if the greatest energy threshold which is
indicative of the highest amount of energy being present is triggered,
then the smallest window size may be utilized. If the next largest energy
threshold is triggered, then the next smallest window size may be
utilized. This comparison results in the selection of the smallest window
size which corresponds to the highest threshold of the oscillatory energy
being triggered.

[0051] If the result of act A34 is negative, then the processing proceeds
to an act A38 to analyze the damping estimated in analysis function
processing 46 with respect to a plurality of damping thresholds which
also correspond to the respective window sizes. A relatively less amount
of data may be processed for a desired accuracy if there is a relatively
decreased amount of damping present in the oscillation energy being
analyzed in one embodiment. Damping thresholds are selected based upon
engineering studies of historical data and/or benchmark testing of the
power system in one example.

[0052] At an act A40, it is determined whether the damping present
triggered (e.g., is less than) any of the damping thresholds.

[0053] If the result of act A40 is positive, then the processing proceeds
to act A36 to select the appropriate window size of the data to be
utilized. For example, if the smallest damping threshold which is
indicative of the least damping being present is triggered, then the
smallest window size may be utilized. If the next smallest damping
threshold is triggered, then the next smallest window size may be
utilized. This comparison results in the selection of the smallest window
size which corresponds to the smallest threshold of the damping being
triggered.

[0054] If the result of act A40 is negative, then the processing proceeds
to an act A42 where the largest window (e.g., default window size) and
corresponding amount of data is utilized to provide the estimation of the
mode. A relatively less amount of data may be processed for a desired
accuracy if there is a relatively smaller amount of damping present in
the oscillation energy being analyzed in one embodiment as mentioned
above.

[0055] The process of FIG. 5 may be continuously performed, and
accordingly different window sizes of data of the signal may be selected
at different times for use in monitoring the oscillation energy of the
signal and corresponding to the information present in the signal at the
different moments in time.

[0056] The window size of data which is processed may be referred to as a
parameter of the analysis function. As discussed above according to one
embodiment, a plurality of values (e.g., 10 sec.-60 min.) of the
parameter may be provided, and one of the values may be selected
corresponding to the content of the signal (e.g., amount of energy
present or damping as discussed above).

[0057] The appropriate estimation of the mode (e.g., frequency and
damping) may be determined from the respective processing operations
40a-40n as selected by the results selection processing 50 described
above in one embodiment. In another embodiment, only a single processing
operation 40 may be performed following the identification of the
appropriate window size without having to estimate the mode a plurality
of times as described in the example of FIG. 3.

[0058] The utilization of different amounts of data in the analysis
function improves the response time and consistency of the analysis
function while maintaining a desired level of accuracy compared with
other approaches which typically have overly slow response times to
changing mode conditions. At different moments in time, the computing
device may estimate the modes differently based upon the content of the
oscillation signal at the different moments in time to provide improved
response times (e.g., faster compared with other static approaches) while
maintaining a desired level of accuracy.

[0059] As discussed above in the above-described example embodiment, modal
energy at a modal frequency of interest and damping may be analyzed
during the result selection processing 50 to determine whether a window
size of data less than a default window size may be utilized. The
above-mentioned example embodiment analyzes filtered data and an RMS
indicator to determine modal energy at a modal frequency of interest.
Other analysis operations may be used in other embodiments. For example,
result selection processing 50 may examine modal energy content using a
power spectral density technique, an oscillation trigger technique, a
ringdown detector technique, or a FFT technique. In addition, the result
selection processing 50 may also utilize information regarding whether
the system was being exposed to active probing during the analysis period
to determine the appropriate estimate of the mode to be used.
Furthermore, the result selection processing 50 may also choose a mode
meter analysis algorithm which best matches a current condition of the
grid in one embodiment, for example, based upon whether or not probing is
occurring or not.

[0060] The estimation of the oscillatory mode (e.g., frequency and
damping) may be output 54 following the selection of the appropriate
estimation of the oscillatory mode. As also shown in FIG. 3, the size of
the window selected in the result selection 50 is applied at processing
52 to the time-series data being passed to mode shape estimation 53. For
example, if result selection processing 50 selected a 10-minute window,
the processing 52 uses a 10-minute window.

[0061] The output of processing 52 as well as the output of the result
selection 50 are provided to mode shape estimation processing 53. Mode
shape processing 53 may improve the accuracy of the mode shape estimated
in FIG. 4 (and which estimation may also be utilized in subsequent
executions of FIG. 4 with respect to the mode of interest). The
estimation of the mode shape provides information (e.g., phases)
regarding the generators which may be participating in the mode and may
be adjusted if there is a need to take corrective action (e.g., reduce or
increase power generation) to mitigate a dangerous mode, such as an
underdamped mode. Improving the accuracy of the mode shape may provide
increased information with respect to identification of the specific
generators which are participating within a mode compared with less
refined mode shape information which may only identify a region of the
electric power grid which contains the participating generator(s) as well
as other generator(s) which are not participating in the mode. The
determined mode shape may assist operators with taking proper action with
respect to specific individual generators to reduce potentially dangerous
modes.

[0062] The mode shape may be estimated using auto and cross-spectral
calculations of a plurality of synchrophasor signals or cross transfer
function estimations of a plurality of synchrophasor signals. After the
auto/cross spectrums or transfer functions are calculated, they may be
evaluated at the mode frequency. Additional details regarding calculating
mode shape are discussed in D. J. Trudnowski, "Estimating
electromechanical mode shape from synchrophasor measurements," IEEE
Transactions on Power Systems, vol. 23, no. 3, pp. 1188-1195, August
2008; L. Dosiek, J. W. Pierre, D. J. Trudnowski, and N. Zhou, "A channel
matching approach for estimating electromechanical mode shape and
coherence," in Proceedings of the 2009 IEEE PES General Meeting, Calgary,
AB, Canada, July 2009; N. Zhou, L. Dosiek, D. Trudnowski, and J. W.
Pierre, "Electromechanical mode shape estimation based on transfer
function identification using PMU measurements," in Proceedings of the
2009 IEEE PES General Meeting, Calgary, AB, Canada, July 2009; and F. K.
Tuffner, L. Dosiek, J. W. Pierre, and D. Trudnowski, "Weighted update
method for spectral mode shape estimation from PMU measurements," in
Proceedings of the 2010 IEEE PES General Meeting, Minneapolis, Minn.,
July 2010, the teachings of which are incorporated herein by reference.
However, these techniques may become computationally burdensome for
real-time automated applications if estimations of mode shape of a
plurality of locations of monitoring devices 18 are to be performed.

[0063] According to one embodiment, a method is disclosed which provides
an estimation of the mode shape without performing cross/auto spectrum
processing of the full frequency spectrum. In this described example, the
spectrum is not calculated at the full spectrum but rather at frequency
bin(s) closest to the frequency of the mode of interest determined by the
selected analysis function 46a-n. For example, result selection 50
selects a mode at 0.2722 Hz and the frequency resolution of the discrete
Fourier calculation is 0.01 Hz, then the auto/cross spectrums are
calculated at 0.27 Hz and 0.28 Hz and averaged using a weighting to bias
to 0.2722 Hz.

[0064] In example embodiments, a sliding-window (e.g., 4-5 minutes of
data) single-bin Discrete Fourier Transform (DFT) technique or a weighted
averaged single-bin DFT technique with a forgetting factor may be
utilized. A single-bin DFT may be computed using a direct DFT
calculation, the Goertzel algorithm or a Chirp-z transform in example
embodiments.

[0065] In one embodiment, the mode shape is continuously calculated (e.g.,
every five seconds) using updated information from the appropriate
analysis functions 46a-n. Furthermore, the modal frequency of interest
may also change during different estimates of the mode shape according to
the output of the result selection processing 50 which results in the
processing of the signal at different frequencies of interest at
different moments in time. While the present embodiment is discussed with
respect to use of a composite signal to calculate mode shape, the mode
shape calculations may also be performed upon other signals, such as
synchrophasors.

[0066] In compliance with the statute, the invention has been described in
language more or less specific as to structural and methodical features.
It is to be understood, however, that the invention is not limited to the
specific features shown and described, since the means herein disclosed
comprise preferred forms of putting the invention into effect. The
invention is, therefore, claimed in any of its forms or modifications
within the proper scope of the appended claims appropriately interpreted
in accordance with the doctrine of equivalents.

[0067] Further, aspects herein have been presented for guidance in
construction and/or operation of illustrative embodiments of the
disclosure. Applicant(s) hereof consider these described illustrative
embodiments to also include, disclose and describe further inventive
aspects in addition to those explicitly disclosed. For example, the
additional inventive aspects may include less, more and/or alternative
features than those described in the illustrative embodiments. In more
specific examples, Applicants consider the disclosure to include,
disclose and describe methods which include less, more and/or alternative
steps than those methods explicitly disclosed as well as apparatus which
includes less, more and/or alternative structure than the explicitly
disclosed structure.